The midfielder, 22, has joined Cordoba this week - becoming the last of four Zidane brothers to leave Real.
Theo posted to social media: "Today it's time to say goodbye to the club of my life, Real Madrid. I joined as a youngest 14 years ago and today I can say that I leave as a man. This has been my home, my school, my family.
"I have grown as a footballer and as a person and I will always carry with me the values that this club has transmitted to me. I want to thank each coach, all the club's workers and each of the teammates I have had, some of whom have become as a friend.
"Every moment shared, every teaching and every learning received has been special for me. Now this stage comes to an end and new doors open along the way. I will always carry a piece of this wherever I go. The shield in my heart.
"Hala Madrid!"